We collect here the definitions and useful properties of modified Bessel functions. The literature is huge as regards these special functions and we may refer the reader to [1]}, [2]} for a nice introduction. The modified Bessel functions of first and second kind are defined as follows
\(I_{\nu }(z)\triangleq \sum _{m=0}^{+\infty }\frac{\left(\frac{z}{2}\right)^{\nu +2m}}{m!\Gamma (\nu +m+1)},\mbox{ }\quad |\mbox{arg}(z)|<\pi \) 
